Use the recursively defined geometric sequence a1=56

, an=4an−1
and find the common ratio.

1 answer

In a geometric sequence, the common ratio \( r \) is the factor by which we multiply each term to get the next term.

Given the recursively defined geometric sequence:

  • The first term \( a_1 = 56 \)
  • The recursive definition \( a_n = 4a_{n-1} \)

From the recursive relation, we can see that each term is obtained by multiplying the previous term by 4.

Thus, the common ratio \( r \) for this geometric sequence is:

\[ r = 4 \]

Therefore, the common ratio of the sequence is \( 4 \).